Luis A. Afonso
Posts:
4,743
From:
LIsbon (Portugal)
Registered:
2/16/05


Re: Chisquared to normal approximation
Posted:
May 19, 2013 9:10 AM


A (perhaps futile) caution note
Back to Wilson and Hilferty formula to convert normal data into Chisquared variable, namely: W= [(Y/r)^(1/p)  (1 2*p^2/r]/sqrt(2*p^2/r)________(1) where y ~ Chisquared, r degrees of freedom, W~ N(0,1), p=3. Solving for y, Y = r *[W*sqrt(2*p^2/r) + (1 2*p^2/r]^p = = r *[W*sqrt(2/(9*r)) + (1 2/(9*r)]^3 Note that this equation allows, for example, to transform, whatever sum of squared deviations from W~N (mu, sigma): n, that follows rigorously a Chisquared r1 df, into normal Data. Referring to (1), as Matthew Shultz states, W doesn´t transform Chisquared variable into a Student one. The reason is clear (1) is a relationship (approximate) between random variables and so has nothing to do with sample mean values . . . He says (wrongly): ___That is, if Z is a standard normal variable, P(Z<W(y)) approx. = P(Y<y). So W(Y) approximates a t statistic___END OF QUOTING.
Luis A. Afonso

